This paper studies the geometry problems with a pure vector tool. The geometry and vector problems can be transformed into each other, and this paper establishes the corresponding vector geometry theory to completely solve this transformation problem, covering the Cartesian coordinate method. A new, independent, complete mathematics system is formed, which leads to a lot of new methods and problems. From a geometric point of view to generalize the fundamental vector theorem, the fundamental vector theorem would have a precise geometric interpretation. From the solid geometry perspective, it not only solves a number of calculation, proof and mapping problems in the application process, and also enriches the connotation of the Euclidean space.